Butterfly Pitch Angle Distributions Research Articles

Formation of Electron Butterfly Pitch Angle Distributions in Saturn's Magnetosphere Due To Scattering by Equatorial ECH Waves

AbstractThe features of electron pitch angle distributions (PADs) often imply different physical mechanisms in planetary magnetospheres. We report a simultaneous equatorial electrostatic electron cyclotron harmonic (ECH) wave event with butterfly PADs of electrons at L ∼ 7.6–9 observed by the Cassini spacecraft. Via calculating the bounce‐averaged electron diffusion rates, we found that Saturnian ECH waves can resonate with ∼10 eV to several keV electrons at <60° pitch angles at time scales from ∼10−8 to 10−4 s−1. Simulations show that the formation of ∼100 eV to ∼1 keV electron butterfly PADs are mainly caused by the pitch angle scattering of electrons at low pitch angles (<30°) and the momentum scattering at intermediate pitch angles of ∼30°–45°, though previous studies suggested the adiabatic transport is the dominated mechanism. Additionally, our results successfully reproduce the variation of peak pitch angles (αp) and phase space density ratios between α90° and αp with L‐shell.

Evidence of Electron Acceleration via Nonlinear Resonant Interactions with Whistler-mode Waves at Foreshock Transients

Shock waves are sites of intense plasma heating and charged particle acceleration. In collisionless solar wind plasmas, such acceleration is attributed to shock drift or Fermi acceleration but also to wave–particle resonant interactions. We examine the latter for the case of electrons interacting with one of the most commonly observed wave modes in shock environments, the whistler mode. Such waves are particularly intense in dynamic, localized regions upstream of shocks, arising from the kinetic interaction of the shock with solar wind discontinuities. These regions, known as foreshock transients, are also sites of significant electron acceleration by mechanisms not fully understood. Using in situ observations of such transients in the Earth’s foreshock, we demonstrate that intense whistler-mode waves can resonate nonlinearly with >25 eV solar wind electrons and accelerate them to ∼100–500 eV. This acceleration is mostly effective for the 50–250 eV energy range, where the accelerated electron population exhibits a characteristic butterfly pitch-angle distribution consistent with theoretical predictions. Such nonlinear resonant acceleration is very fast, implying that this mechanism may be important for injecting suprathermal electrons of solar wind origin into the shock region, where they can undergo further, efficient shock-drift acceleration to even higher energies.

Photoelectron Butterfly Pitch-angle Distributions in the Martian Ionosphere Based on MAVEN Observations

Using pitch-angle-resolved electron fluxes recorded by the Mars Atmosphere and Volatile Evolution spacecraft over 5 yr, we present a detailed analysis of the occurrence patterns of photoelectron butterfly pitch-angle distributions (PADs) in the Martian ionosphere. Statistical analysis indicates that Martian photoelectron butterfly PADs favorably occur near the moderate crustal magnetic fields with a strength of 10–30 nT on the dayside and 10–15 nT on the nightside. The nightside occurrence rates are much higher. Furthermore, dayside butterfly PADs prefer to occur near the vertical magnetic field lines in the ionosphere, and the significant day-to-night transport of photoelectrons evades the nightside strongest magnetic anomaly regions. These features strongly support the idea that Martian photoelectron butterfly PADs are more likely to occur in eclipse or near the terminator and that they mainly form due to the adiabatic evolution of photoelectrons that transport along the closed cross-terminator magnetic field lines. Despite the negligible energy dependence in the darkness, the occurrence rate of dayside butterfly PADs observed at higher altitudes and near the subsolar region increases with energy, presumably related to the increased proportion of electrons from the solar wind when measured at relatively higher electron energies, which, however, is limitedly understood and deserves future investigation. Our comprehensive observations suggest the diverse influence of Martian magnetic topology on the ionospheric plasma in different spatial regions, and, in turn, analysis of their influence allows us a better understanding of the intricate Martian global magnetic system.

Storm-Time Evolution of the Equatorial Electron Pitch Angle Distributions in Earth’s Outer Radiation Belt

In this study we analyze the storm-time evolution of equatorial electron pitch angle distributions (PADs) in the outer radiation belt region using observations from the Magnetic Electron Ion Spectrometer (MagEIS) instrument aboard the Van Allen Probes in 2012–2019. The PADs are approximated using a sum of the first, third and fifth sine harmonics. Different combinations of the respective coefficients refer to the main PAD shapes within the outer radiation belt, namely the pancake, flat-top, butterfly and cap PADs. We conduct a superposed epoch analysis of 129 geomagnetic storms and analyze the PAD evolution for day and night MLT sectors. PAD shapes exhibit a strong energy-dependent response. At energies of tens of keV, the PADs exhibit little variation throughout geomagnetic storms. Cap PADs are mainly observed at energies<300 keV, and their extent in L shrinks with increasing energy. The cap distributions transform into the pancake PADs around the main phase of the storm on the nightside, and then come back to their original shapes during the recovery phase. At higher energies on the dayside, the PADs are mainly pancake during pre-storm conditions and become more anisotropic during the main phase. The quiet-time butterfly PADs can be observed on the nightside at L>5.6. During the main phase, butterfly PADs have stronger 90°-minima and can be observed at lower L-shells (down to L = 5), then transitioning into flat-top PADs at L ∼ 4.5 – 5 and pancake PADs at L<4.5. The resulting PAD coefficients for different energies, locations and storm epochs can be used to test the wave models and physics-based radiation belt codes in terms of pitch angle distributions.

Statistical Characteristics of Energetic Electron Pitch Angle Distributions in the Van Allen Probe Era: 1. Butterfly Distributions With Flux Peaks at Preferred Pitch Angles

AbstractWe present a statistical study on the properties of equatorial electron pitch angle distributions (PADs) in the Earth's outer radiation belt, for the first time based on particle measurements from the entire Van Allen Probes mission. A detailed selection criteria is used to identify intervals when flux measurements at energies from 0.2 to 3.4 MeV are available across a wide range of pitch angles close to the geomagnetic equatorial plane. To better characterize the shape of each pitch angle distribution, the flux data is fitted to functions of the equatorial pitch angle based on Legendre polynomials. Using this technique, we show that the shape of the PADs strongly depends on the particle's energy, location and geomagnetic activity. These results are used to identify the dominant physical processes responsible for creating PADs with different shapes. The results presented here mainly focus on the occurrence statistics and properties of butterfly PADs. Significantly, we find clear evidence that butterfly PADs have a peak flux that preferentially occurs at two distinct and discrete equatorial pitch angles, either 35° ± 5° or 65° ± 5°. Energy, L‐shell and magnetic local time variations indicate that the flux peaks at equatorial pitch angles ∼35° appear consistent with magnetopause shadowing, whilst those peaking at ∼65° may be associated with wave‐particle interactions. We also show that the flux at low and high pitch angles, for both butterfly and nonbutterfly PADs, remains remarkably well correlated even as the flux intensity varies by four orders of magnitude.

Cassini Observation of Relativistic Electron Butterfly Distributions in Saturn’s Inner Radiation Belts: Evidence for Acceleration by Local Processes

AbstractThe morphology of electron pitch angle distributions (PADs) helps to identify dynamic processes in Saturn’s magnetosphere. Previous studies demonstrated convective transport being important for relativistic electron acceleration at L > 4 in the inner magnetosphere, whereas closer to Saturn the situation is not as well established. We have investigated the PADs of relativistic electrons throughout radiation belts, using 13‐years measurements from Cassini spacecraft. Our results show that at 3.5 < L < 6, the PADs peak near 90°. However, at 2.5 < L < 3.5, the PADs transform to butterfly distributions, dominating over an energy range of one order of magnitude, from 800 keV to >7 MeV. These results suggest that convective transport continues to govern down to L = 3.5. For even smaller L‐shells, the independence of butterfly PADs from energy suggests that the acceleration by resonant interactions of electrons with waves likely serves as an additional key mechanism regulating the dynamics in the core region of radiation belts.

Numerical simulation of chorus-driving acceleration of relativistic electrons at extremely low L-shell during geomagnetic storms* *Project supported by the National Natural Science Foundation of China (Grant Nos. 41904149 and 12173038), Stable-Support Scientific Project of ChinaResearch Institute of Radiowave Propagation (Grant No. A132001W07), and the National Institute of Natural Hazards, Ministry of Emergency Management of China (Grant No. 2021-JBKY-11).

During 2018 major geomagnetic storm, relativistic electron enhancements in extremely low L-shell regions (reaching L∼3) have been reported based on observations of ZH-1 and Van Allen probes satellites, and the storm is highly likely to be accelerated by strong whistler-mode waves occurring near very low L-shell regions where the plasmapause was suppressed. It is very interesting to observe the intense chorus-accelerated electrons locating in such low L-shells and filling into the slot region. In this paper, we further perform numerical simulation by solving the two-dimensional Fokker–Planck equation based on the bounce-averaged diffusion rates. Numerical results demonstrate the evolution processes of the chorus-driven electron flux and confirm the flux enhancement in low pitch angle ranges (20°–50°) after the wave-particle interaction for tens of hours. The simulation result is consistent with the observation of potential butterfly pitch angle distributions of relativistic electrons from both ZH-1 and Van Allen probes.

Equatorial Pitch Angle Distributions of 1–50 keV Electrons in Earth's Inner Magnetosphere: An Empirical Model Based on the Van Allen Probes Observations

AbstractUsing 7 years of data from the Helium, Oxygen, Proton, and Electron instrument on the Van Allen Probes, equatorial pitch angle distributions (PADs) of 1–50 keV electrons in Earth's inner magnetosphere are investigated statistically. An empirical model of electron equatorial PADs as a function of radial distance, magnetic local time, geomagnetic activity, and electron energy is constructed using the method of Legendre polynomial fitting. Model results show that most equatorial PADs of 1–10s of keV electrons in Earth's inner magnetosphere are pancake PADs, and the lack of butterfly PADs is likely due to their relatively flat or positive flux radial gradients at higher altitudes. During geomagnetically quiet times, more anisotropic distributions of 1–10s of keV electrons at dayside than nightside are observed, which could be responsible for moderate chorus wave activities at dayside during quiet times as reported by previous studies. During active times, the anisotropy of 1–10s of keV electrons significantly enhances, consistent with the enhanced chorus wave activity during active times and suggesting the critical role of 1–10s of keV electrons in generating chorus waves in Earth's inner magnetosphere. Different enhanced anisotropy patterns of different energy electrons are also observed during active times: at R > ∼4 RE, keV electrons are more anisotropic at dawn to noon, while 10s of keV electrons have larger anisotropy at midnight to dawn. These differences, combined with the statistical distribution of chorus waves shown in previous studies, suggest the differential roles of electrons with different energies in generating chorus waves with different properties.

Parametric Dependence of the Formation of Electron Butterfly Pitch Angle Distribution Driven by Magnetosonic Waves

AbstractUsing the full relativistic test particle (TP) simulation code, we investigate the parametric dependence of electron scattering and phase space density evolution driven by magnetosonic (MS) waves at L = 4.5 both inside and outside the plasmapause. The scattering effects caused by Landau resonance, bounce resonance, and the transit‐time effect are all involved in the study. The net scattering effects are evaluated in the form of diffusion coefficients with different combinations of MS wave parameters, such as frequency bandwidth and wave normal angle, and ambient plasma density. The results demonstrate that (1) Landau resonance and the transit‐time effect dominate the electron scattering inside and outside the plasmapause, respectively, while both are modulated by bounce resonant scattering; (2) bounce resonant scattering becomes more important with narrowband MS waves; (3) electron scattering induced by MS waves is highly sensitive to wave normal angle. The temporal phase space density (PSD) evolution obtained from 2‐D kinetic Fokker‐Planck simulations shows that MS waves with larger wave normal angles are more likely to generate electron butterfly pitch angle distributions (PADs) for hundreds of keV electrons outside the plasmapause. Our study suggests that the electron butterfly distribution has important implications for revealing the combined scattering of MS wave‐particle interactions, and the combination of the multiple scattering mechanisms should be carefully incorporated in future global modeling of radiation belt dynamics.

Distinct Formation and Evolution Characteristics of Outer Radiation Belt Electron Butterfly Pitch Angle Distributions Observed by Van Allen Probes

AbstractUsing Van Allen Probes pitch angle‐resolved electron flux data, we report intriguing events of electron butterfly pitch angle distributions (PADs) at L > ~5.5 on the nightside with distinct durations, i.e., about 9 hr for the 28–29 April 2013 event and over 2 days for the 2–5 May 2013 event. The formation and evolution of the short‐duration electron butterfly PADs exhibited insignificant dependence on electron energy, probably resulting from a combination of drift shell splitting, magnetopause shadowing, and wave diffusion, but the long‐duration electron butterfly evolution presented strong energy dependence, likely mainly attributed to interactions with MS waves. Both the short‐duration and long‐duration electron butterfly PADs disappeared closely related to enhanced substorm activities, while the responsible waves could be plasmaspheric hiss or chorus waves. Our results demonstrate that radiation belt electron butterfly PADs are naturally complex in both spatial and temporal scales and well connected to solar wind condition, substorm activity, and magnetospheric wave distribution.

On the loss mechanisms of radiation belt electron dropouts during the 12 September 2014 geomagnetic storm

Radiation belt electron dropouts indicate electron flux decay to the background level during geomagnetic storms, which is commonly attributed to the effects of wave-induced pitch angle scattering and magnetopause shadowing. To investigate the loss mechanisms of radiation belt electron dropouts triggered by a solar wind dynamic pressure pulse event on 12 September 2014, we comprehensively analyzed the particle and wave measurements from Van Allen Probes. The dropout event was divided into three periods: before the storm, the initial phase of the storm, and the main phase of the storm. The electron pitch angle distributions (PADs) and electron flux dropouts during the initial and main phases of this storm were investigated, and the evolution of the radial profile of electron phase space density (PSD) and the (<italic>μ</italic>, <italic>K</italic>) dependence of electron PSD dropouts (where <italic>μ</italic>, <italic>K</italic>, and <italic>L</italic>* are the three adiabatic invariants) were analyzed. The energy-independent decay of electrons at <italic>L</italic> &gt; 4.5 was accompanied by butterfly PADs, suggesting that the magnetopause shadowing process may be the major loss mechanism during the initial phase of the storm at <italic>L</italic> &gt; 4.5. The features of electron dropouts and 90°-peaked PADs were observed only for &gt;1 MeV electrons at <italic>L</italic> &lt; 4, indicating that the wave-induced scattering effect may dominate the electron loss processes at the lower <italic>L</italic>-shell during the main phase of the storm. Evaluations of the (<italic>μ</italic>, <italic>K</italic>) dependence of electron PSD drops and calculations of the minimum electron resonant energies of H⁺-band electromagnetic ion cyclotron (EMIC) waves support the scenario that the observed PSD drop peaks around <italic>L</italic>* = 3.9 may be caused mainly by the scattering of EMIC waves, whereas the drop peaks around <italic>L</italic>* = 4.6 may result from a combination of EMIC wave scattering and outward radial diffusion.

Statistical Study of Energetic Electron Butterfly Pitch Angle Distributions During Magnetic Dip Events

AbstractThe magnetic dips can create the electron butterfly pitch angle distribution (PAD) in the inner magnetosphere. However, its universality is still unconfirmed. We statistically investigate the global distribution of the occurrence rate of the magnetic dip‐related butterfly PAD for 466 keV and 2.1 MeV electrons using the measurements of the twin Van Allen Probes spanning from September 2012 to November 2018. The statistical results show that the magnetic dip‐related butterfly PADs are mainly confined to duskside to midnight within 4.5 &lt; L &lt; 6, and the peak occurrence rate (30% for 466 KeV and 70% for 2.1 MeV) occurs at the duskside equator around L = 5. The parametric study results suggest that the butterfly PADs preferably occur for high energy electrons with a negative initial radial flux gradient and a nearly isotropic initial PAD, which is consistent with the statistic results. This work confirms the vital importance of the magnetic dips on the evolution of the electron PADs.

Modeling the Electron Flux Enhancement and Butterfly Pitch Angle Distributions on L Shells &lt;2.5

AbstractWe analyze an energetic electron flux enhancement event in the inner radiation belt observed by Van Allen Probes during an intense geomagnetic storm. The energetic electron flux at L~1.5 increased by a factor of 3 with pronounced butterfly pitch angle distributions (PADs). Using a three‐dimensional radiation belt model, we simulate the electron evolution under the impact of radial diffusion, local wave‐particle interactions including hiss, very low frequency transmitters, and magnetosonic waves, as well as Coulomb scattering. Consistency between observation and simulation suggests that inward radial diffusion plays a dominant role in accelerating electrons up to 900 keV and transporting the butterfly PADs from higher L shells to form the butterfly PADs at L~1.5. However, local wave‐particle interactions also contribute to drive butterfly PADs at L ≳ 1.9. Our study provides a feasible mechanism to explain the electron flux enhancement in the inner belt and the persistent presence of the butterfly PADs at L~1.5.

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

AbstractIn this paper, we presented two observational cases and simulations to indicate the relationship between the formation of butterfly‐like electron pitch angle distributions and the emission of low‐harmonic (LH) fast magnetosonic (MS) waves inside the high‐density plasmasphere. In the wave emission region, the pitch angle of relativistic (&gt;1 MeV) electrons becomes obvious butterfly‐like distributions for both events (near‐equatorially mirroring electrons are transported to lower pitch angles). Unlike relativistic (&gt;1 MeV) electrons, energetic electrons (&lt;1 MeV) change slightly, except that relatively low‐energy electrons (&lt;~150 keV) show butterfly‐like distributions in the 21 August 2013 event. In theory, the LH MS waves can affect different‐energy electrons through the bounce resonance, Landau resonance, and transit time scattering. By performing the Fokker‐Planck diffusion simulations, we demonstrate that the bounce resonance with the LH MS waves mainly leads to the butterfly pitch angle distribution of MeV electrons, whereas the Landau resonance and transit time scattering mainly affect energetic electrons in the high‐density region.

On the Contribution of EMIC Waves to the Reconfiguration of the Relativistic Electron Butterfly Pitch Angle Distribution Shape on 2014 September 12—A Case Study*

Abstract Following the arrival of two interplanetary coronal mass ejections on 2014 September 12, the Relativistic Electron–Proton Telescope instrument on board the twin Van Allen Probes observed a long-term dropout in the outer belt electron fluxes. The interplanetary shocks compressed the magnetopause, thereby enabling the loss of relativistic electrons in the outer radiation belt to the magnetosheath region via the magnetopause shadowing. Previous studies have invoked enhanced radial transport associated with ultra-low-frequency waves activity and/or scattering into the atmosphere by whistler mode chorus waves to explain electron losses deep within the magnetosphere (L &lt; 5.5). We show that energetic electron pitch angle distributions (PADs) provide strong evidence for precipitation also via interaction with electromagnetic ion cyclotron (EMIC) waves. High-resolution magnetic field observations on Van Allen Probe B confirm the sporadic presence of EMIC waves during the most intense dropout phase on September 12. Observational results suggest that magnetopause shadowing and EMIC waves together were responsible for reconfiguring the relativistic electron PADs into peculiar butterfly PAD shapes a few hours after an interplanetary shock arrived at Earth.

Formation of Butterfly Pitch Angle Distributions of Relativistic Electrons in the Outer Radiation Belt With a Monochromatic Pc5 Wave

AbstractRadial transport of relativistic electrons in the inner magnetosphere has been considered one of the acceleration mechanisms of the outer radiation belt electrons and can be driven by the drift resonance with Pc5 ultralow‐frequency waves. In this study, we focus on the pitch angle dependences of the radial transport and investigate the pitch angle distributions (PADs) of the relativistic electrons after interaction with a monochromatic Pc5 wave, using two simulation models of the inner magnetosphere: Geomagnetic Environment Modeling System for Integrated Studies (GEMSIS)‐Ring Current and GEMSIS‐Radiation Belt models. The results show that butterfly‐like PADs (two peaks in small pitch angles) are produced at a fixed radial distance (L‐shell) and energy, where the electrons with small pitch angles satisfy the resonance condition. The radial range and timescale of the butterfly PAD appearance correspond to the maximum radial transport of the electron (i.e., resonant width) and its oscillation period in the radial direction, respectively. We analytically derive the resonant width and oscillation period of relativistic electrons interacting with a monochromatic Pc5 wave, assuming conservation of first and second adiabatic invariants, and compare them with the simulation result. The results show that electrons with small equatorial pitch angles at a fixed magnetic moment can interact with a monochromatic Pc5 wave in a wider L‐shell range than perpendicular electrons due to the pitch angle changes, in the course of the radial transport.

Relativistic electron's butterfly pitch angle distribution modulated by localized background magnetic field perturbation driven by hot ring current ions

AbstractDayside modulated relativistic electron's butterfly pitch angle distributions (PADs) from ∼200 keV to 2.6 MeV were observed by Van Allen Probe B at L = 5.3 on 15 November 2013. They were associated with localized magnetic dip driven by hot ring current ion (60–100 keV proton and 60–200 keV helium and oxygen) injections. We reproduce the electron's butterfly PADs at satellite's location using test particle simulation. The simulation results illustrate that a negative radial flux gradient contributes primarily to the formation of the modulated electron's butterfly PADs through inward transport due to the inductive electric field, while deceleration due to the inductive electric field and pitch angle change also makes in part contribution. We suggest that localized magnetic field perturbation, which is a frequent phenomenon in the magnetosphere during magnetic disturbances, is of great importance for creating electron's butterfly PADs in the Earth's radiation belts.

A positive correlation between energetic electron butterfly distributions and magnetosonic waves in the radiation belt slot region

AbstractEnergetic (hundreds of keV) electrons in the radiation belt slot region have been found to exhibit the butterfly pitch angle distributions. Resonant interactions with magnetosonic and whistler‐mode waves are two potential mechanisms for the formation of these peculiar distributions. Here we perform a statistical study of energetic electron pitch angle distribution characteristics measured by Van Allen Probes in the slot region during a 3 year period from May 2013 to May 2016. Our results show that electron butterfly distributions are closely related to magnetosonic waves rather than to whistler‐mode waves. Both electron butterfly distributions and magnetosonic waves occur more frequently at the geomagnetically active times than at the quiet times. In a statistical sense, more distinct butterfly distributions usually correspond to magnetosonic waves with larger amplitudes and vice versa. The averaged magnetosonic wave amplitude is less than 5 pT in the case of normal and flat‐top distributions with a butterfly index BI =1 but reaches ∼50–95 pT in the case of distinct butterfly distributions with BI &gt;1.3. For magnetosonic waves with amplitudes &gt;50 pT, the occurrence rate of butterfly distribution is above 80%. Our study suggests that energetic electron butterfly distributions in the slot region are primarily caused by magnetosonic waves.

Rapid flattening of butterfly pitch angle distributions of radiation belt electrons by whistler‐mode chorus

AbstractVan Allen radiation belt electrons exhibit complex dynamics during geomagnetically active periods. Investigation of electron pitch angle distributions (PADs) can provide important information on the dominant physical mechanisms controlling radiation belt behaviors. Here we report a storm time radiation belt event where energetic electron PADs changed from butterfly distributions to normal or flattop distributions within several hours. Van Allen Probes observations showed that the flattening of butterfly PADs was closely related to the occurrence of whistler‐mode chorus waves. Two‐dimensional quasi‐linear STEERB simulations demonstrate that the observed chorus can resonantly accelerate the near‐equatorially trapped electrons and rapidly flatten the corresponding electron butterfly PADs. These results provide a new insight on how chorus waves affect the dynamic evolution of radiation belt electrons.

Wave-driven butterfly distribution of Van Allen belt relativistic electrons.

Van Allen radiation belts consist of relativistic electrons trapped by Earth's magnetic field. Trapped electrons often drift azimuthally around Earth and display a butterfly pitch angle distribution of a minimum at 90° further out than geostationary orbit. This is usually attributed to drift shell splitting resulting from day–night asymmetry in Earth's magnetic field. However, direct observation of a butterfly distribution well inside of geostationary orbit and the origin of this phenomenon have not been provided so far. Here we report high-resolution observation that a unusual butterfly pitch angle distribution of relativistic electrons occurred within 5 Earth radii during the 28 June 2013 geomagnetic storm. Simulation results show that combined acceleration by chorus and magnetosonic waves can successfully explain the electron flux evolution both in the energy and butterfly pitch angle distribution. The current provides a great support for the mechanism of wave-driven butterfly distribution of relativistic electrons.